Author:
Mironov A.,Morozov A.,Zenkevich Y.
Abstract
AbstractWe demonstrate that the symmetric elliptic polynomials $$E_\lambda (x)$$
E
λ
(
x
)
originally discovered in the study of generalized Noumi–Shiraishi functions are eigenfunctions of the elliptic Ruijsenaars–Schneider (eRS) Hamiltonians that act on the mother function variable $$y_i$$
y
i
(substitute of the Young-diagram variable $$\lambda $$
λ
). This means they are eigenfunctions of the dual eRS system. At the same time, their orthogonal complements in the Schur scalar product, $$P_\lambda (x)$$
P
λ
(
x
)
are eigenfunctions of the elliptic reduction of the Koroteev–Shakirov (KS) Hamiltonians. This means that these latter are related to the dual eRS Hamiltonians by a somewhat mysterious orthogonality transformation, which is well defined only on the full space of time variables, while the coordinates $$x_i$$
x
i
appear only after the Miwa transform. This observation explains the difficulties with getting the apparently self-dual Hamiltonians from the double elliptic version of the KS Hamiltonians.
Funder
Russian Science Foundation
Publisher
Springer Science and Business Media LLC
Subject
Physics and Astronomy (miscellaneous),Engineering (miscellaneous)
Reference57 articles.
1. F. Calogero, J. Math. Phys. 12, 419 (1971)
2. B. Sutherland, Phys. Rev. A 5, 1372 (1972)
3. J. Moser, Adv. Math. 16, 197–220 (1975)
4. M. Olshanetsky, A. Perelomov, Phys. Peps. 71, 313 (1981)
5. M. Olshanetsky, A. Perelomov, Phys. Rep. 94, 6 (1983)
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